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Geometric Range Searching and Its Relatives
 CONTEMPORARY MATHEMATICS
"... ... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems. ..."
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Cited by 273 (41 self)
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... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems.
The buffer tree: A new technique for optimal I/Oalgorithms
 University of Aarhus
, 1995
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External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 76 (32 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
The Buffer Tree: A Technique for Designing Batched External Data Structures
, 2003
"... We present a technique for designing external memory data structures that support batched operations I/O efficiently. We show how the technique can be used to develop external versions of a search tree, a priority queue, and a segment tree, and give examples of how these structures can be used to d ..."
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Cited by 75 (14 self)
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We present a technique for designing external memory data structures that support batched operations I/O efficiently. We show how the technique can be used to develop external versions of a search tree, a priority queue, and a segment tree, and give examples of how these structures can be used to develop I/Oefficient algorithms. The developed algorithms are either extremely simple or straightforward generalizations of known internal memory algorithms—given the developed external data structures.
ExternalMemory Algorithms for Processing Line Segments in Geographic Information Systems
, 2007
"... In the design of algorithms for largescale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this paper we develop ..."
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Cited by 67 (25 self)
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In the design of algorithms for largescale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient externalmemory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red–blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them.
New Upper Bounds in Klee's Measure Problem (Extended Abstract)
, 1988
"... We give new upper bounds for the measure problem of Klee which significantly improve the previous bounds for dimensions greater than 2. We obtain an O(n d/2 log n, n logn) timespace upper bound to compute the measure of a set of n boxes in Euclidean &space. The solution requires several new ..."
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Cited by 56 (0 self)
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We give new upper bounds for the measure problem of Klee which significantly improve the previous bounds for dimensions greater than 2. We obtain an O(n d/2 log n, n logn) timespace upper bound to compute the measure of a set of n boxes in Euclidean &space. The solution requires several new ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of dspace.
Faster SMetric Calculation by Considering Dominated Hypervolume as Klee’s Measure Problem
, 2006
"... The dominated hypervolume (or Smetric) is a commonly accepted quality measure for comparing approximations of Pareto fronts generated by multiobjective optimizers. Since optimizers exist, namely evolutionary algorithms, that use the Smetric internally several times per iteration, a faster determi ..."
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Cited by 38 (2 self)
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The dominated hypervolume (or Smetric) is a commonly accepted quality measure for comparing approximations of Pareto fronts generated by multiobjective optimizers. Since optimizers exist, namely evolutionary algorithms, that use the Smetric internally several times per iteration, a faster determination of the Smetric value is of essential importance. This paper describes how to consider the Smetric as a special case of a more general geometrical problem called Klee’s measure problem (KMP). For KMP, an algorithm exists with run time O(n logn + n d/2 log n), for n points of d ≥ 3 dimensions. This complex algorithm is adapted to the special case of calculating the Smetric. Conceptual simplifications of the implementation are concerned that save on a factor of O(logn) and establish an upper bound of O(n logn + n d/2) for the Smetric calculation, improving the previously known bound of O(n d−1).
Efficient ExternalMemory Data Structures and Applications
, 1996
"... In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oeffic ..."
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Cited by 37 (9 self)
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In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oefficient algorithms through the design of I/Oefficient data structures. One of our philosophies is to try to isolate all the I/O specific parts of an algorithm in the data structures, that is, to try to design I/O algorithms from internal memory algorithms by exchanging the data structures used in internal memory with their external memory counterparts. The results in the thesis include a technique for transforming an internal memory tree data structure into an external data structure which can be used in a batched dynamic setting, that is, a setting where we for example do not require that the result of a search operation is returned immediately. Using this technique we develop batched dynamic external versions of the (onedimensional) rangetree and the segmenttree and we develop an external priority queue. Following our general philosophy we show how these structures can be used in standard internal memory sorting algorithms